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Broodless winter break varroa cycle?

My first hive had a varroa problem that I did not become wise to until late fall when it was too cold to treat. They made a new queen very late due to the failure of the original and I am pretty sure she never mated--saw no eggs or brood at the last inspectin in Nov, about two weeks after she first emerged, and none as of two days ago. She has survived the winter with a decent sized cluster and the hive went broodless all winter. Should a broodless winter (at least 3 full months) eliminate the varroa problem? I would have thought so but I saw a couple of bees with mites on their backs. I have a package with a new queen ordered in case the queen never gets going but I am wondering if I should leave the surviving bees (and possibly surviving mites) in the hive when I add the package. Could a few survivng mites start a new infestation or are they too old to reproduce now? A sugar dusting or two should be pretty effective since it is a small population with no emerging brood to support a new generation of mites. Any other insights or suggestions?

3 month without brood doesn’t solve the Varroa problem. They can live up to 6 month on bees and start again. You will also have NO guarantee that the new package is mite free. I would treat the leftover hive and the package with OA vapor at least one time. Remember you can treat with OA vapor even during winter as long as the temperatures a few degrees above freezing.
I would not add the package to the old colony. There might be an old queen and the trouble can start.
Remove the old queen first and the next day put the package on top with a sheet of newspaper between.
If you can’t find the old mom place the new colony on the place where the old hive is and brushes all bees from the old hive nearby in the grass. Bees will find the way home but the queen has no orientation. To be on the save way, you can also put a queen excluder in front of the entrances.
Check out whether it is worth to save the old colony, there all bees from last year and die in a few week anyway.

You made the last inspection last November, check now; maybe they have a brood nest. Depends on your location, in cold areas they can stop breeding even the end of October.

They can last months with no brood, and do you really know that the bees are broodless anyway? After doing numerous winter inspections, I don't think my strain is ever completely broodless. Some do have broodless periods, but I don't know how long for.

If you break the brood cycle all mite has to come out of the cells and sitting on bees. This is the only way to kill them with OA in one treatment.
Tests are made and the result after one OA vapor treatment was mostly over 95%. OA doesn’t penetrate wax and you can’t reach Varroa during summer when they breeding.

Make a split in summer before swarming and take the old queen away in a 5 frame nuc. Bees starting with queen cells and after 7 days cut all cells except one.

Now they breeding a new queen and it take 17 day before the queen hatched. Another 5 days and she is ready for the mating flight, at least one more day before the new mom start laying eggs and up to 5 more days where you can treat against Varroa.

After 24 days all the brood hatched (incl. drones) and there is no way for the Varroa to hide. Treat the hive the 25th or 26th day after you removed the old queen and the Varroa trouble for the whole year is over, except your bee neighbor is lazy and your bees coming with a backpack.

Why the old mom in a nuc? Sometimes the new get lost during mating and you can give them the old mom back.

Michael Bush made a good analogy here one time
he breeds horses
is you breed the mare every year, how many horses will you have in 10 years?
if you breed her every other year how many will you have?
way less
breaking the brood cycle doesn't eliminate mites, it just reduces their population. kind of an IPM thing
there are times of the year that it doesn't really help bees to raise brood but they do it anyway (around here, in July and August). make them stop and the mites can't multiply

I had one hive of Russians a couple of years ago. During a dearth they completely stopped brood production while my Italians just backed off a little. Same over winter...little to no brood. Is this the mechanism Russians use to fight varroa? Not on purpose but co-incidentally.

the bioliogical growth (curve) of varroa and histroic data on survival of hives suggest that it takes two years for varroa to kill a hive starting off from a low level of infestation.

breaking the brood cycle will somewhat affect the growth profile of varroa.

a better analogy might be the differce between continuous compounding interest and interest that is only calculate ones a year (or period). the end results of continuous compounding intest... of calcualting interest on top of interest although by appearace may look minimal the cumulative (additive) effect can be huge.

this same reasoning is the primary reason I rake drone brood in the early spring. it does not cure the varroa problem but it does interrup the varroa's growth cycle.

I have done a full inspection and I am 100% confident that there are no eggs or brood. I feel pretty certain that the queen never mated in the fall and based on the responses to a question in the queen/breeding forum, I don't think she can or will mate since she is now about 4 months old.

I know that 100% mite elimination is unrealistic but I guess this is a great opportunity to treat the adult bees.

I have done a full inspection and I am 100% confident that there are no eggs or brood. I feel pretty certain that the queen never mated in the fall and based on the responses to a question in the queen/breeding forum, I don't think she can or will mate since she is now about 4 months old.

I know that 100% mite elimination is unrealistic but I guess this is a great opportunity to treat the adult bees.

Your new pkgs

Start them on your best brood comb & pollen/honey frames from losses but don't combine with the old failures they're worthless now. Your colonies' success depends on the quality of the new queen don't mix with 2nd class citizens.

She emerged in November and the weather turned pretty crumby right about the time she would be mating--most hives were expelling drones for weeks before that. I saw no eggs or brood on my last inspection in the fall and none when I was in the hive recently. The queen looked pretty small and slender.

It has all become a bit of a moot point since I started this post. The survivors and queen were finished off by robbers last week. There was not a single live bee in my hive and some hastily torn open cappings on the frame closest to the reduced entrance with big bits of wax on the bottom board below.